Mikel Arteta admits Arsenal are "gutted" about their Champions League exit, but must show they can "turn their season around" against Wolves live on Sky Sports.
Joshua Kimmich's header in the second half saw the Germans to a 1-0 victory in the quarter-final second leg, winning 3-2 on aggregate.
It comes after a damaging 2-0 defeat to Aston Villa in the Premier League last weekend saw them lose ground in the title race.
But Arteta says despite the disappointment, on Thursday morning, attentions will turn to their league game against Wolves live on Saturday Night Football. The Premier League is the only trophy left for Arsenal to win this season.
The Gunners boss said: "We have to be close to the players. What they need to do is stand right next to them, give them our support and our love.
"We have to pick it up because we have a big, big game on Saturday. We really want it and we have to show that we're capable of turning it around.
"We have to go through the pain tonight and tomorrow, get up and come with the same attitude we had here, and hopefully beat Wolves."
Arteta provided some clarity to the exit as well, adding that it can takes team years to reach the semi-finals and beyond.
"At the moment it is a really gutted dressing room," he told TNT Sports. "I cannot find the right words to lift them. I wish I had. We have to go through it.
"The club has been without Champions League football for seven years and you want to play in the first year and be in the semi-finals or the final.
"We all wanted that so badly but you can see in many other clubs it takes them sometimes six or seven years to get to that stage.
"We tried against a team who has a lot of experience and through the tie the margins have been very small. There were moments where we were better.
"We gave them two goals and in the tie that was a big advantage to give away.
You could see there was zero margin for error and we made a big mistake defending the box to concede the goal. Then it was difficult. We tried in many different ways but it's difficult."
Analysis: Just the start for Arsenal in Champions League
Sky Sports' Oliver Yew:
Another chance of silverware slipped from Arsenal's grasp in Munich.
It was another disappointing night for the Gunners following their defeat to Aston Villa on Sunday, which handed Man City the initiative in the Premier League title race.
However, while Sunday's result left the Emirates Stadium flat and deflated as hopes of winning a first Premier League title since 2003/04 suffered a setback, defeat in Europe can be a crucial part of the building and learning process for Mikel Arteta's young side as they look to become a real force in the Champions League.
"We have to go through the pain," Arteta said after the 1-0 defeat at the Allianz Arena, which saw the Gunners crash out of the tournament 3-2 on aggregate. "The club has been without Champions League football for seven years and you want to play in the first year and be in the semi-finals or the final. We all wanted that so badly, but you can see in many other clubs it takes them sometimes six or seven years to get to that stage. But we were very close, that's the reality."
Manchester City didn't make it out of the group stage in their two appearances in the Champions League. They reached one semi-final in their first eight goes at it. They reached the final in their 10th crack at it and only lifted the trophy at the 13th attempt.
The point is it takes time and there's no shame in a quarter-final exit at the hands of Bayern Munich, who reached a 14th semi-final in the competition.
Arsenal's lack of experience showed in this tie as they handed the initiative to Bayern at a crucial time in the first leg when they were dominant. They switched off for a split second in the second and they were punished. Arteta said it himself: "There was zero margin."
But just as sides have gone through it before them in Europe's premier club competition, this young Arsenal side will learn from this. Arteta will learn from this, and the challenge is to keep building, keep improving and going on the trajectory they have been, and come back stronger for another crack next season.